Question

A group of naturalists catch, tag and release 121 trout into a lake. The next day they catch and release 48 trout, of which 22 had been tagged. Using this ratio, how many trout would be estimated to be in the lake?

Answer 1

264 trouts are estimated to be in the lake.

Using proportion, we write: Tagged trout/Total Trout

This becomes 22/48.

In order to use cross multiplication, we write another fraction using x, the total number of trout in the lake: 121/x.

Now we have 121/x=22/48.

We cross multiply.

121*48=22x.

(121*48)/22 becomes:

264.

Answer 2

264.

Explanation:

Let x represent the number of trout in the lake.

We have been given that a group of naturalists catch, tag and release 121 trout into a lake. The next day they catch and release 48 trout, of which 22 had been tagged.

Using proportions, we will get:

`\frac{\text{Total trouts}}{\text{Tagged trouts}}=(48)/(22)`

`(x)/(121)=(48)/(22)`

`(x)/(121)*121=(48)/(22)*121`

`x=(24)/(11)*121`

`x=24*11`

`x=264`

Therefore, there would be approximately 264 trout in the lake.